APPLIED PHYSICS LETTERS 97, 143114 共2010兲
Orientation-dependent work function of graphene on Pd„111…
Y. Murata,1 E. Starodub,2 B. B. Kappes,3 C. V. Ciobanu,3 N. C. Bartelt,2 K. F. McCarty,2
and S. Kodambaka1,a兲
1
Department of Materials Science and Engineering, University of California Los Angeles, Los Angeles,
California 90095, USA
2
Sandia National Laboratories, Livermore, California 94550, USA
3
Division of Engineering, Colorado School of Mines, Golden, Colorado 80401, USA
共Received 28 July 2010; accepted 10 September 2010; published online 7 October 2010兲
Selected-area diffraction establishes that at least six different in-plane orientations of monolayer
graphene on Pd共111兲 can form during graphene growth. From the intensities of low-energy electron
microscopy images as a function of incident electron energy, we find that the work functions of the
different rotational domains vary by up to 0.15 eV. Density functional theory calculations show that
these significant variations result from orientation-dependent charge transfer from Pd to graphene.
These findings suggest that graphene electronics will require precise control over the relative
orientation of the graphene and metal contacts. © 2010 American Institute of Physics.
关doi:10.1063/1.3495784兴
Graphene, a two-dimensional crystalline sheet of
carbon,1 has generated considerable attention owing to its
ultrathin geometry, high carrier mobility,2 and tunable band
gap,3 with potential applications in high-performance lowpower electronics4 and as transparent electrodes.5 Since
graphene-based devices require metal 共or metallic兲 contacts,
knowledge of the electronic properties, for example, nature
of the contact 共Ohmic or Schottky兲 and electron transport at
the metal–graphene interfaces is essential. Previous theoretical studies of graphene-metal contacts indicated that their
electronic properties depend on the graphene–metal interaction energies.6 For example, strongly interacting metals can
induce a charge transfer from or to graphene, resulting in por n-type doping, respectively.6 Here, using Pd共111兲 as a
model substrate,7 we focus on understanding the influence of
metal substrate and the in-plane orientation of graphene on
its work function. Using a combination of in situ low-energy
electron microscopy 共LEEM兲 共Ref. 8兲 and density functional
theory 共DFT兲 calculations we show that monolayer graphene
on Pd共111兲 exhibits a work function that varies significantly
with domain orientation, a result of spatial variations in
charge transfer at the graphene–Pd interface. Our results suggest that a precise control over graphene orientation with
respect to the metal contacts is essential for the realization of
large-scale graphene electronics.
In our experiments, the Pd共111兲 single-crystal substrate
was first saturated with carbon by annealing at ⬃900 ° C
overnight in a tube furnace in a flow of 90% Ar–10% CH4 at
760 Torr. Sample temperature in the LEEM was measured
using a type-C thermocouple spot-welded to a washer in intimate thermal contact with the crystal. The surface was
cleaned by cycles of sputtering using 1.5 keV Ar+ and annealing at ⬃900 ° C. Monolayer graphene was grown by
cooling from ⬃900 to 790 ° C at the rate of ⬃1 K / s, a
well-established process used to segregate C from the bulk to
the surface.9–11 The sample was then quenched to room temperature for analysis. To determine graphene layer thickness
and work function,12,13 LEEM image intensities I versus
a兲
Author to whom correspondence should be addressed. Electronic mail:
kodambaka@ucla.edu.
0003-6951/2010/97共14兲/143114/3/$30.00
electron energy E data were acquired at 0.1 eV intervals
between E = −5 and 30 eV and 0.01 eV intervals between
E = 0 and 2.5 eV.
Figure 1共a兲 is a representative LEEM image from
Pd共111兲 covered with monolayer graphene. The spatial variations in image contrast, as we show below, result from different rotational domains of graphene, each with its own
characteristic electron reflectivity. Selected-area low-energy
electron diffraction 共LEED兲 共Ref. 14兲 measurements yielded
at least six distinct patterns 关see Fig. 2共a兲兴, indicative of a
polycrystalline film. In Fig. 2共a兲, the sixfold symmetric spots
highlighted by two arrows correspond to Pd共111兲-1 ⫻ 1 and
graphene-1 ⫻ 1 lattices, respectively. In all patterns, the
graphene is rotated with respect to the substrate. The angles
of rotation ␪ are ⫺2°, ⫺5°, ⫺10°, +17°, +22°, and +26°
with a measurement uncertainty of ⫾1°. ␪ is the angle between Pd关110兴 and graphene 关112̄0兴 with the positive 共negative兲 sign denoting in-plane clockwise 共counterclockwise兲
rotation. Figure 1共b兲 shows the six domains color-coded,
with the 22°-rotated domain being the most abundant. The
inner sets of sixfold symmetric spots in Fig. 2 indicate ordered superstructures whose periodicities ␭ are larger than
the graphene and Pd lattice constants. These structures are
moiré patterns resulting from superposing the graphene and
Pd共111兲 lattices. Similar patterns occur for graphene on other
FIG. 1. 共Color online兲 共a兲 LEEM image of monolayer graphene on Pd共111兲.
Field of view is 14.5 ␮m and E = 17.7 eV. 共b兲 Graphene domains colorcoded using the color scheme of Fig. 2.
97, 143114-1
© 2010 American Institute of Physics
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143114-2
Murata et al.
Appl. Phys. Lett. 97, 143114 共2010兲
FIG. 2. 共Color online兲 共a兲 LEED patterns of the six graphene domains with rotational angles ␪ = −2°, ⫺5°, ⫺10°, +17°, +22°, and +26°. Dashed and solid
arrows show Pd关110兴 and graphene 关112̄0兴 directions, respectively. 共b兲 Atomic models of Pd共111兲 共darker contrast spheres兲 and graphene layers 共lighter
contrast spheres兲 rotated by ␪c = −2.1°, ⫺5.7°, ⫺11°, +14°, +19°, and +26°. Rhombi highlight the unit cells of each moiré pattern. The arrow is Pd关110兴.
lattice-mismatched substrates.15 From LEED, we measure
␭ = 22 Å, 17 Å, 12 Å, 8 Å, 7 Å, and 19 Å with accuracies of
⫾1 Å, respectively, for ␪ = 2°, 5°, 10°, 17°, 22°, and 26°.
To gain better insight into the moiré patterns, we constructed atomic models of each domain assuming that the
graphene and Pd lattices are commensurate. Under this constraint, the graphene layer is stretched or contracted by
0.1%–2.5% to lattice match the Pd sites, and ␭c values were
calculated for each orientation ␪c from 0° to 60°.16 We obtain
good agreement between the calculated and experimental ␭
values for ␪c = 2.1°, 5.7°, 11°, 14°, 19°, and 26°, which yield
␭c = 21.8 Å, 17.2 Å, 12.6 Å, 9.9 Å, 7.3 Å, and 19.2 Å, respectively. Figure 2共b兲 shows the atomic models, whose surface unit cells are 共3 冑 7 ⫻ 3 冑 7兲-R19°, 共冑39⫻ 冑 39兲-R16°,
共冑21⫻ 冑 21兲-R11°, 共冑13⫻ 冑 13兲-R14°, 共冑7 ⫻ 冑 7兲-R19°, and
共7 ⫻ 7兲.
We now focus on how in-plane orientation affects electronic structure. In LEEM, all electrons are specularly reflected from the sample for sufficiently low incident electron
energies E. When E exceeds the difference between the work
functions of the electron gun filament ⌽fil and the sample
surface ⌽surface, the reflected intensity I decreases due to
electron–surface interactions. Hence, we used I versus E data
to determine ⌽surface 共Ref. 12兲 for the different graphene orientations. Figure 3共a兲 plots I normalized to the intensity I0 at
E = 0 eV, with the solid and dashed curves denoting monolayer graphene domains and clean Pd共111兲, respectively. The
ratio I / I0 decreases from unity to 0.9 at an energy ␸, the
electron injection threshold energy, that is characteristic of
the work function. For all the six graphene domains, ␸ is
⬃1.3 eV lower than the value corresponding to clean
Pd共111兲, showing that graphene substantially decreases the
work function. The high-resolution plot in Fig. 3共b兲 reveals
that the work functions ⌽G of the different domains are not
the same. In fact, they differ by up to 0.15 eV.
To compare with absolute work functions in the
literature, we calibrate following the procedure described
in Ref. 17 and references therein. For clean Pd共111兲, we
measure ␸ = 2.2⫾ 0.1 eV. The literature value of ⌽Pd
= 5.3– 5.6 eV.9,18 Then, ⌽fil 共=⌽Pd − ␸兲 = 3.1– 3.4 eV. Simi-
larly, we determine ⌽G for each domain from the solid
curves in Fig. 3. Our knowledge of ⌽Pd limits the accuracies
of ⌽G to ⫾0.15 eV. However, the work function differences
are precise to ⫾0.02 eV. Choosing ⌽Pd = 5.6 eV and ⌽fil
= 3.4 eV yields ⌽G values between 4.25 and 4.42 eV for the
different graphene domains. The orientation-averaged value
具⌽G典 is 4.3⫾ 0.1 eV, in good agreement with previous
results.9 In comparison, ⌽ = 4.5 eV for free-standing
graphene.6
To understand the effect of Pd substrate and the
graphene orientation on its work function, we performed
DFT calculations in the local density approximation using
ultrasoft pseudopotentials.19 From the variation in the local
FIG. 3. 共Color online兲 共a兲 Normalized image intensity 共I / I0兲 vs E for
graphene domains with ␪ = 2°, 5°, 10°, 17°, 22°, and 26°. Dashed curve is
clean Pd共111兲. 共b兲 Magnified view of rectangle in 共a兲, with the x-axis shifted
by the work function of the electron gun filament ⌽fil = 3.4 eV. The vertical
dotted lines show the range of ⌽. 共c兲 Computed planar average of electron
transfer density ⌬n vs normal coordinate z for ␪ = 19°. The dashed line
within the graphene–Pd interface shows the integration limit for the effective transferred charge q. 共d兲 Contour plots of ⌬n in the plane half-way
between graphene and the top Pd layer for ␪ = 19° and 30°.
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143114-3
Appl. Phys. Lett. 97, 143114 共2010兲
Murata et al.
potential through a supercell of six Pd共111兲 layers and 12 Å
vacuum, we find ⌽Pd = 5.59 eV, consistent with previous
calculations.6 DFT simulations with periodic boundary conditions require the graphene layer to be commensurate with
Pd共111兲, so we keep graphene at its equilibrium lattice constant 共2.445 Å兲 and strain the substrate accordingly. Since the
strain value is specific to each orientation ␪, the effects of
strain and ␪ on ⌽G cannot be separated. Thus, we focus on
the domain with the lowest strain, ␪ = 19°. We calculate ⌽G
= 4.14 eV for this orientation, which is smaller than that of
free-standing graphene, consistent with our experiments. We
attribute this work function decrease to the formation of an
effective dipole layer oriented away from the substrate.20
This dipole results from the transferred electron density
around the surface, which has an oscillatory character and
integrates to a positive charge q toward vacuum and -q toward the substrate 关Fig. 3共c兲兴. We also calculated ⌽G for ␪
= 5.7° and 10.9°, finding values lower than free-standing
graphene despite large substrate strains 共⬃1% – 5%兲. These
results are consistent with recent calculations for ␪ = 30°
showing similar surface dipoles.6
We gain insight into the physical origin of the
orientation-dependence of the work function from the contour plots in Fig. 3共d兲, which compare the electronic transfer
in the plane midway between graphene and the first Pd layer
for ␪ = 19° and 30°. For the latter orientation, which has sixfold in-plane symmetry, the integrated transferred charge q is
0.0092 e / C atom. This value is different from that of the 19°
orientation, 0.0105 e / C atom. Clearly, the oscillatory behavior of the transferred charge is sensitive to changes in bonding at the graphene–Pd interface and varies with in-plane
orientation of graphene. As a result, the strength of the effective dipole layer, and hence the work function varies with
domain orientation.
In conclusion, we observed six rotational domains of
monolayer graphene on Pd共111兲, whose work functions are
all different and lower than that of free-standing graphene.
Our calculations suggest that this orientation dependence
arises from spatial variations in charge transfer at the
graphene–Pd interface. We expect similar phenomenon for
graphene on other metals, although the magnitude of work
function variation may depend on the strength of the
graphene–metal interactions. Therefore, a precise control
over the relative orientation between graphene and metal
contacts is desirable for the large-scale fabrication of
graphene devices.
Work at Sandia was supported by the Office of Basic
Energy Sciences, Division of Materials Sciences and Engineering of the U.S. DOE under Contract No. DE-AC0494AL85000. We acknowledge support from Northrop Grumman and UC Discovery grant, and from the NSF through
Grants Nos. CMMI-0825592 and CMMI-0846858.
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